The presumptive GOP nominee’s slow start in Ohio could undermine his chances of winning the White House

Though Donald Trump dispensed with his last primary opponent months before Hillary Clinton will, the presumptive Republican presidential nominee trails far behind the leading Democrat in organizing in key general-election states.

Ohio, a state that has backed every presidential winner since 1964, presents both Mr. Trump’s best opportunity to carry a big swing state and reveals his team’s steep logistical challenges.

After winning the GOP nomination on a tight budget with a skeletal staff, Mr. Trump doesn’t have any general-election staff in the state, and senior aides in New York and Washington haven’t made contact with the state Republican Party. Efforts to recruit the state’s experienced operatives who helped elect Gov. John Kasich have so far been unsuccessful, people familiar with the matter said.

Mrs. Clinton has a small team of full-time aides in Ohio, where they are working to rebuild the organization that twice carried the state for President Barack Obama.

“It’s like we’re all at ground zero,” said Ed Rollins, who is co-chairman of the pro-Trump super PAC called the Great America PAC. “I think we have a superior candidate. It’s a question of whether you can build the resources. Campaigns are used to building for two years, and we have far less time to do it.”

Mr. Trump’s slow start, here and elsewhere, could undermine his goal of expanding the Republican presidential map into the industrial Midwest and breaking up a voting bloc that has given the Democrats an advantage for nearly a decade.